Mutations of fake weighted projective spaces. (English) Zbl 1432.52023
Summary: We characterise mutations between fake weighted projective spaces, and give explicit formulas for how the weights and multiplicity change under mutation. In particular, we prove that multiplicity-preserving mutations between fake weighted projective spaces are mutations over edges of the corresponding simplices. As an application, we analyse the canonical and terminal fake weighted projective spaces of maximal degree.
MSC:
| 52B20 | Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) |
| 14J33 | Mirror symmetry (algebro-geometric aspects) |
| 14J45 | Fano varieties |
Keywords:
lattice polytopes; mutations; cluster transformations; mirror symmetry; Fano varieties; canonical singularities; terminal singularities; projective spaceReferences:
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